Another quilt - size?

I have put the Jinny Beyer quilt away for the moment. My patience has run out for the moment. To do something totally opposite I started piecing a string quilt I have been collecting strips for. I thought I might use it as a 'charity' quilt (for a child). I made the blocks 9" (finished size), so the quilt is about 36" x 45". Is that too small? I don't think I have enough strips to increase another row each way. I am reluctant to put a border on it but have got a fabric that may be suitable. Because I used calico as a backing for the blocks I am concerned that if I add a border it will be relatively 'thin' compared to the centre (if you understand what I am getting at). The other concern is how do I quilt it? Maybe I should have made it quilt-as-you-go but I didn't want strips between the blocks as I wanted the impact of the blocks butting right up to each other... anyway it is too late for that now!